Ronen Peretz - The Krzyż Conjecture: Theory and Methods

Ronen Peretz

Ben Gurion University of the Negev, Israel

Published by

World Scientific Publishing Co. Pte. Ltd.

5 Toh Tuck Link, Singapore 596224

USA office:27 Warren Street, Suite 401-402, Hackensack, NJ 07601

UK office:57 Shelton Street, Covent Garden, London WC2H 9HE

Library of Congress Cataloging-in-Publication Data

Names: Peretz, Ronen, author.

Title: The Krzyz conjecture : theory and methods / Ronen Peretz, Ben Gurion University of the Negev, Israel.

Description: Hackensack, NJ : World Scientific, [2021] | Includes bibliographical references and index.

Identifiers: LCCN 2020038651 (print) | LCCN 2020038652 (ebook) | ISBN 9789811226373 (hardcover) | ISBN 9789811226380 (ebook for institutions) | ISBN 9789811226397 (ebook for individuals)

Subjects: LCSH: Analytic functions.

Classification: LCC QA331 .P379 2021 (print) | LCC QA331 (ebook) | DDC 515/.73--dc23

LC record available at https://lccn.loc.gov/2020038651

LC ebook record available at https://lccn.loc.gov/2020038652

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library.

Copyright 2021 by World Scientific Publishing Co. Pte. Ltd.

All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

For any available supplementary material, please visit
https://www.worldscientific.com/worldscibooks/10.1142/11993#t=suppl

Desk Editors: Jing Wen Soh/George Vasu

Typeset by Stallion Press
Email:

Printed in Singapore

Dedicated to my beloved ones Noam, Ruth and Amos.

This is Noam

Noam and his mom

Ronen Peretzis a faculty member in the department of mathematics at Ben Gurion University of the Negev in Beer Sheva, Israel. His areas of research include Geometric Function Theory, Extremal Problems in Complex Functions Theory, Affine Geometry related to polynomial mappings. In applied mathematics, he is an expert in digital image processing.

Bounded analytic functions and in particular those that are defined on the open unit disc, U, are among the most important functions in complex function theory of one complex variable. The amount of research on those functions is enormous. It dates back to the early stages of classical function theory and is still vivid and central in modern mathematics. A classical book on this subject is titled Bounded Analytic Functions by John B. Garnett. Many general problems on complex analytic functions can be reduced to the bounded analytic functions. Hence, the significance of pursuing further the study of bounded analytic functions. Even if we restrict attention to those bounded analytic functions that are defined on U